Context and Background¶
AllLife Bank is a US bank that has a growing customer base. The majority of these customers are liability customers (depositors) with varying sizes of deposits. The number of customers who are also borrowers (asset customers) is quite small, and the bank is interested in expanding this base rapidly to bring in more loan business and in the process, earn more through the interest on loans. In particular, the management wants to explore ways of converting its liability customers to personal loan customers (while retaining them as depositors).
A campaign that the bank ran last year for liability customers showed a healthy conversion rate of over 9% success. This has encouraged the retail marketing department to devise campaigns with better target marketing to increase the success ratio.
You as a Data scientist at AllLife bank have to build a model that will help the marketing department to identify the potential customers who have a higher probability of purchasing the loan.
Objective:¶
- To predict whether a liability customer will buy a personal loan or not.
- Which variables are most significant.
- Which segment of customers should be targeted more.
Dataset:¶
- ID: Customer ID
- Age: Customer’s age in completed years
- Experience: #years of professional experience
- Income: Annual income of the customer (in thousand dollars)
- ZIP Code: Home Address ZIP code.
- Family: the Family size of the customer
- CCAvg: Average spending on credit cards per month (in thousand dollars)
- Education: Education Level. 1: Undergrad; 2: Graduate;3: Advanced/Professional
- Mortgage: Value of house mortgage if any. (in thousand dollars)
- Personal_Loan: Did this customer accept the personal loan offered in the last campaign?
- Securities_Account: Does the customer have securities account with the bank?
- CD_Account: Does the customer have a certificate of deposit (CD) account with the bank?
- Online: Do customers use internet banking facilities?
- CreditCard: Does the customer use a credit card issued by any other Bank (excluding All life Bank)?
Importing necessary libraries¶
In [1]:
# this will help in making the Python code more structured automatically (good coding practice)
%load_ext nb_black
# Library to suppress warnings or deprecation notes
import warnings
warnings.filterwarnings("ignore")
# Libraries to help with reading and manipulating data
import pandas as pd
import numpy as np
# Library to split data
from sklearn.model_selection import train_test_split
# libaries to help with data visualization
import matplotlib.pyplot as plt
import seaborn as sns
# Removes the limit for the number of displayed columns
pd.set_option("display.max_columns", None)
# Sets the limit for the number of displayed rows
pd.set_option("display.max_rows", 200)
# Library to build Logistic Regression Classifier
from sklearn.linear_model import LogisticRegression
# Libraries to build decision tree classifier
from sklearn.tree import DecisionTreeClassifier
from sklearn import tree
# To tune different models
from sklearn.model_selection import GridSearchCV
# To get diferent metric scores
from sklearn.metrics import (
f1_score,
accuracy_score,
recall_score,
precision_score,
confusion_matrix,
plot_confusion_matrix,
make_scorer,
roc_auc_score,
precision_recall_curve,
roc_curve,
)
Examining and Inspecting the dataset¶
Read the dataset¶
In [2]:
loan_df = pd.read_csv("Loan_Modelling.csv")
In [4]:
# copying data to another varaible to avoid any changes to original data
data = loan_df.copy()
View the first and last 5 rows of the dataset.¶
In [5]:
data.head() # first 5 rows of the dataset
Out[5]:
In [6]:
data.tail() # last 5 rows of the dataset
Out[6]:
Comments:¶
- The target column is the Personal_Loan attribute which specifies if the customer has taken a loan or not.
- The ID variable is in serial order, unique value to the dataset and shows no relationship with the target variable. Attribute will need to be dropped in the data prep phase.
- Zip Code is a nominal variable that needs to be mapped to the county dimension
- Ordinal Categorical variables are Family and Education
- Binary categorical variables are CD_Account, Security_Account, Online, Credit_card. This needs to be transformed to categorical data types.
- Age, Experience, Income, CCAvg and Mortgage are interval variables
Rearranging of the target variable to appear as the last column of the data set¶
In [7]:
p_loan = data["Personal_Loan"]
data.drop(["Personal_Loan"], axis=1, inplace=True)
data["Personal_Loan"] = p_loan
data.head(5)
Out[7]:
Checking the shape of the dataset¶
In [8]:
data.shape
Out[8]:
- The dataset consists of 5000 rows and 14 columns
Check the data types of the columns in the dataset.¶
In [9]:
data.info()
Comments:¶
- No categorical, object or boolen variables. However, the columns 'CD Account', 'Online', 'Family', 'Education' , 'CreditCard' and 'Securities Account' are categorical variable and needs to be transformed.
- Dataset consists of 1 float data type and 13 integers.
Check for duplicates in the data set¶
In [10]:
data[data.duplicated()].count()
Out[10]:
- No duplicates found in the dataset
Check for missing values¶
In [11]:
data.isnull().sum()
Out[11]:
- Also no missing values in the data set
Summary of the dataset¶
In [12]:
data.describe().T
Out[12]:
Comments:¶
- Age seems to be normally distirbuted as the mean and median are almost of same value. Age mean is 45 and the range is between 23 years - 67 years.
- Experience also similar as Age seems to have a normal distirbution. However the minimum experience is -3years which indicates an error issue because years of experience can't be negative
- Average income is approximately \$74. The income range is between \\$8 - \$224. Attribute is skewed to the right. Presence of some outlier.
- CCAVG has mean of 1.93. Range is from 0 -10. Data is skewed to the right.
- Majority of the customers have no mortgage. Distribution is heavily skewed to right
- Categorical variables such as Family, Education,Personal loan, security_account, cd_account,online and credit card all have clean records
Fixing the experience error and decoding the ZipCodes into county dimensions¶
In [13]:
neg_experience = data["Experience"] < 0
neg_experience.value_counts()
Out[13]:
In [14]:
data["Experience"] = data["Experience"].apply(abs)
In [15]:
data[data["Experience"] < 0][
"Experience"
].value_counts() ###checking for negative values
Out[15]:
In [16]:
from uszipcode import SearchEngine
search = SearchEngine()
county = []
for i in np.arange(0, len(data["ZIPCode"])):
zipcode = search.by_zipcode(data["ZIPCode"][i])
if zipcode is not None:
county.append(zipcode.county)
else:
county.append("NoMatch")
data["County"] = county
data.head()
Out[16]:
In [17]:
cat_columns = [
"Family",
"Education",
"Securities_Account",
"CD_Account",
"Online",
"CreditCard",
"Personal_Loan",
"County",
]
for i in cat_columns:
print(data[i].value_counts(normalize=True))
print("-" * 50)
Mapping of Counties to Regions¶
In [23]:
Superior_California = [
"Butte County",
"El Dorado County",
"Yolo County",
"Sacramento County",
"Placer County",
"Shasta County",
"Siskiyou County",
]
North_Coast = [
"Humboldt County",
"Lake County",
"Napa County",
"Trinity County",
"Mendocino County",
"Sonoma County",
]
SanFrancisco = [
"Alameda County",
"Contra Costa County",
"Marin County",
"San Francisco County",
"San Mateo County",
"Santa Clara County",
"Solano County",
]
Northern_San_Joaquin = [
"Alpine County",
"Amador County",
"Calaveras County",
"Madera County",
"Mariposa County",
"Merced County",
"Mono County",
"San Joaquin County",
"Stanislaus County",
"Tuolumne County",
]
Central_Coast = [
"Monterey County",
"San Benito County",
"San Luis Obispo County",
"Santa Barbara County",
"Santa Cruz County",
"Ventura County",
]
Southern_San_Joaquin = [
"Fresno County",
"Inyo County",
"Kern County",
"Kings County",
"Tulare County",
]
Inland_Empire = ["Riverside County", "San Bernardino County"]
Los_Angeles = ["Los Angeles County"]
Orange = ["Orange County"]
SanDiego = ["San Diego County", "Imperial County"]
other = ["NoMatch"]
In [24]:
def region_combining(x):
if x in Superior_California:
return "Superior_California"
elif x in North_Coast:
return "North_Coast"
elif x in SanFrancisco:
return "SanFrancisco"
elif x in Northern_San_Joaquin:
return "Northern_San_Joaquin"
elif x in Central_Coast:
return "Central_Coast"
elif x in Southern_San_Joaquin:
return "Southern_San_Joaquin"
elif x in Inland_Empire:
return "Inland_Empire"
elif x in Los_Angeles:
return "Los_Angeles"
elif x in Orange:
return "Orange"
elif x in SanDiego:
return "SanDiego"
elif x in other:
return "other"
else:
return x
In [25]:
data["region"] = data["County"].apply(region_combining)
In [26]:
print("Distinct values in Region column:", data.region.unique())
In [27]:
data.region.value_counts(normalize=True)
Out[27]:
Exploratory Data Analysis¶
Univariate Analysis for Interval Variables¶
In [28]:
def histogram_boxplot(data, feature, figsize=(15, 10), kde=False, bins=None):
"""
Boxplot and histogram combined
data: dataframe
feature: dataframe column
figsize: size of figure (default (15,10))
kde: whether to show the density curve (default False)
bins: number of bins for histogram (default None)
"""
f2, (ax_box2, ax_hist2) = plt.subplots(
nrows=2, # Number of rows of the subplot grid= 2
sharex=True, # x-axis will be shared among all subplots
gridspec_kw={"height_ratios": (0.25, 0.75)},
figsize=figsize,
) # creating the 2 subplots
sns.boxplot(
data=data, x=feature, ax=ax_box2, showmeans=True, color="violet"
) # boxplot will be created and a star will indicate the mean value of the column
sns.histplot(
data=data, x=feature, kde=kde, ax=ax_hist2, bins=bins, palette="winter"
) if bins else sns.histplot(
data=data, x=feature, kde=kde, ax=ax_hist2
) # For histogram
ax_hist2.axvline(
data[feature].mean(), color="green", linestyle="--"
) # Add mean to the histogram
ax_hist2.axvline(
data[feature].median(), color="black", linestyle="-"
) # Add median to the histogram
Age¶
In [29]:
histogram_boxplot(data, "Age")
Comment:¶
- Age column is normally distributed with majority of customers falling between 30 to 60 years of age. Mean is almost equal to the median.
Experience¶
In [30]:
histogram_boxplot(data, "Experience")
Comment:¶
- Experience column also have a normal distribution with more customers having experience starting from 8 years. Mean is approximately equal to the median.
Income¶
In [31]:
histogram_boxplot(data, "Income")
Comment:¶
- Income attribute is postively skewed. There are outliers at the higher scale end.
- Majority of the customers have income between 40k - 90k.
CCAvg¶
In [32]:
histogram_boxplot(data, "CCAvg")
Comment:¶
- CCAvg attribute is right skewed. There are outliers at the higher scale end.
- Majority of customers spend less than 2.5k
Mortgage¶
In [33]:
histogram_boxplot(data, "Mortgage")
Comment:¶
- 70% of the customers have either no mortgage or value less than 40K.
Univariate Analysis for Categorical Variable¶
In [34]:
# function to create labeled barplots
def labeled_barplot(data, feature, perc=False, n=None):
"""
Barplot with percentage at the top
data: dataframe
feature: dataframe column
perc: whether to display percentages instead of count (default is False)
n: displays the top n category levels (default is None, i.e., display all levels)
"""
total = len(data[feature]) # length of the column
count = data[feature].nunique()
if n is None:
plt.figure(figsize=(count + 1, 5))
else:
plt.figure(figsize=(n + 1, 5))
plt.xticks(rotation=90, fontsize=15)
ax = sns.countplot(
data=data,
x=feature,
palette="Paired",
order=data[feature].value_counts().index[:n].sort_values(),
)
for p in ax.patches:
if perc == True:
label = "{:.1f}%".format(
100 * p.get_height() / total
) # percentage of each class of the category
else:
label = p.get_height() # count of each level of the category
x = p.get_x() + p.get_width() / 2 # width of the plot
y = p.get_height() # height of the plot
ax.annotate(
label,
(x, y),
ha="center",
va="center",
size=12,
xytext=(0, 5),
textcoords="offset points",
) # annotate the percentage
plt.show() # show the plot
Family¶
In [35]:
labeled_barplot(data, "Family", perc=True)
Securities Account¶
In [36]:
labeled_barplot(data, "Securities_Account", perc=True)
Personal Loan¶
In [37]:
labeled_barplot(data, "Personal_Loan", perc=True)
CD_Account¶
In [38]:
labeled_barplot(data, "CD_Account", perc=True)
Online¶
In [39]:
labeled_barplot(data, "Online", perc=True)
Credit Card¶
In [40]:
labeled_barplot(data, "CreditCard", perc=True)
Region¶
In [41]:
labeled_barplot(data, "region", perc=True)
Comments:¶
- Distribution of customers cut slightly even across the family size tiers with family of 1 having the highest proportion.
- We have more of undergraduates as customers who can qualify for personal loans.
- Majority of the customers (~90%) do not have security account with the bank.
- Bulk of the customers(~93%) do not have certificates of deposit with the bank.
- 59% of customers do use online banking as their preferred channel.
- Majority of customers (~70%) do not have credit cards with the bank.
- ~10% of customers have taken loan from the bank. There's huge opportunity in this regards.
- Bulk of the customers are located in Los Angeles and San Francisco Bay area.
Bivariate Analysis¶
In [42]:
plt.figure(figsize=(15, 7))
sns.heatmap(data.corr(), annot=True, vmin=-1, vmax=1, cmap="Spectral")
plt.show()
Comments:¶
- Income, CC_Avg and CD_Account have maximum correlation with the target variable (Personal_Loan) in that order.
- Age and Experience are highly correlated and correlation is almost 1. Since Age has higher correlation factor than Experience in relation to the target variable, Experience can be dropped from the dataset during the data prep.
- Income and CC_Avg is moderately correlated.
- Mortgage and Income has moderate correlation of 12%.
- CD_Account has some level of association with Securities Account, Online, CreditCard and Personal Loan.
- Income influences CC_Avg, Mortgage, CD_Account and Personal Loan
In [43]:
plt.figure(figsize=(15, 7))
sns.pairplot(data=data, hue="Personal_Loan")
plt.show()
Comments:¶
- Individuals who have higher income tend to apply for loans. However, this tend to cuts across the age band.
- The higher the Experience, the higher the income.
- Individuals with higher CC_Avg tend to apply for loans.
- Individuals with higher tier of education level have higher income and tend to apply for loans.
Checking the association of Personal_Loan with independent variables¶
Influence of Income and CCAvg on Personal loan¶
In [44]:
plt.figure(figsize=(15, 7))
sns.scatterplot(x="CCAvg", y="Income", hue="Personal_Loan", data=data)
Out[44]:
Comments:¶
- Customers who have taken loans have higher income and CCAvg value. It simply means the higher the CCAvg and Income the more likely customers take up loans
Influence of Income and Mortgage on Personal loan¶
In [45]:
plt.figure(figsize=(15, 7))
sns.scatterplot(x="Mortgage", y="Income", hue="Personal_Loan", data=data)
Out[45]:
Comments:¶
- Customers who have taken loans have higher mortgage and income value.
Customer Level Analysis : Education as reference¶
In [46]:
cols = data[
[
"Income",
"CCAvg",
"Mortgage",
"Experience",
"Age",
]
].columns.tolist()
plt.figure(figsize=(12, 10))
for i, variable in enumerate(cols):
plt.subplot(4, 2, i + 1)
sns.boxplot(
data["Education"],
data[variable],
hue=data["Personal_Loan"],
palette="PuBu",
showfliers=False, # turning-off outliers
)
plt.tight_layout()
plt.legend(loc="upper left", bbox_to_anchor=(1, 1))
plt.title(variable)
plt.show()
Comments:¶
- Customers who took loan have same range of income irrespective of education level.
- Customers with education level of graduate and advanced/professional have higher chances of taking a loan.
- Customers of any education level but with high value of house mortgae, have higher chance of taking a loan compared to those of the same education level but with low house mortgage.
In [47]:
# function to plot stacked bar chart
def stacked_barplot(data, predictor, target):
"""
Print the category counts and plot a stacked bar chart
data: dataframe
predictor: independent variable
target: target variable
"""
count = data[predictor].nunique()
sorter = data[target].value_counts().index[-1]
tab1 = pd.crosstab(data[predictor], data[target], margins=True).sort_values(
by=sorter, ascending=False
)
print(tab1)
print("-" * 120)
tab = pd.crosstab(data[predictor], data[target], normalize="index").sort_values(
by=sorter, ascending=False
)
tab.plot(kind="bar", stacked=True, figsize=(count + 5, 6))
plt.legend(
loc="lower left",
frameon=False,
)
plt.legend(loc="upper left", bbox_to_anchor=(1, 1))
plt.show()
Personal_Loan vs Family¶
In [48]:
stacked_barplot(data, "Family", "Personal_Loan")
Comments :¶
- Family of larger sizes have higher chances of taking up loans.
Personal Loan vs Securities Account¶
In [49]:
stacked_barplot(data, "Securities_Account", "Personal_Loan")
Comments :¶
- There is similar distribution of loan adoption for customers who have security accounts or not.
Personal Loan vs Online¶
In [50]:
stacked_barplot(data, "Online", "Personal_Loan")
Comments:¶
- Similar loan adoption rate for customer who use either online channel or not
Personal Loan vs Region¶
In [51]:
stacked_barplot(data, "region", "Personal_Loan")
Comments:¶
- North Coast Region has the highest loan adoption rate.
Personal Loan vs Credit Card¶
In [52]:
stacked_barplot(data, "CreditCard", "Personal_Loan")
Comments:¶
- Similar loan adoption rate for customer with or without credit cards.
Personal Loan vs CD_Account¶
In [53]:
stacked_barplot(data, "CD_Account", "Personal_Loan")
Comments:¶
- Customers with CD Account have higher chances of collecting loans.
Data Preprocessing¶
- Dropping of the Experience column due to high correlation with Age,ID for non-relevance, ZIPCode and County for derivation of the region column.
- Outlier Treatment(perform capping of outliers).
- All the values smaller than the lower whisker will be assigned the value of the lower whisker, and all the values above the upper whisker will be assigned the value of the upper whisker.
In [54]:
## Dropping the Experience, ID, ZIPCode and County Columns
data.drop(["ID", "ZIPCode", "County", "Experience"], axis=1, inplace=True)
Outlier Detection using boxplot¶
In [55]:
numerical_col = data.select_dtypes(include=np.number).columns.tolist()
plt.figure(figsize=(20, 30))
for i, variable in enumerate(numerical_col):
plt.subplot(5, 4, i + 1)
plt.boxplot(data[variable], whis=1.5)
plt.tight_layout()
plt.title(variable)
plt.show()
- Income, CCAvg and Mortgage have outliers at the upper scale end that needs to be treated.
Outier Treatment¶
In [56]:
# functions to treat outliers by flooring and capping
# Applying the outlier treatment function and excluding the transformed variables and Year, mileage and seats.
p25 = data[["Income", "CCAvg", "Mortgage"]].quantile(0.25) # Lower whisker boundary
p75 = data[["Income", "CCAvg", "Mortgage"]].quantile(0.75) # Upper Whisker Boundary
data[["Income", "CCAvg", "Mortgage"]] = data[["Income", "CCAvg", "Mortgage"]].clip(
p25, p75, axis=1
) # outlier clipping
In [57]:
# let's look at box plot to see if outliers have been treated or not
plt.figure(figsize=(20, 30))
for i, variable in enumerate(numerical_col):
plt.subplot(5, 4, i + 1)
plt.boxplot(data[variable], whis=1.5)
plt.tight_layout()
plt.title(variable)
plt.show()
Data Preparation¶
In [58]:
X = data.drop(["Personal_Loan"], axis=1)
Y = data["Personal_Loan"]
X = pd.get_dummies(X, drop_first=True)
# Splitting data in train and test sets
X_train, X_test, y_train, y_test = train_test_split(
X, Y, test_size=0.30, random_state=1
)
In [59]:
# Splitting data into training and test set:
X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.3, random_state=1)
print(X_train.shape, X_test.shape)
In [60]:
print("Number of rows in train data =", X_train.shape[0])
print("Number of rows in test data =", X_test.shape[0])
In [61]:
print("Percentage of classes in training set:")
print(y_train.value_counts(normalize=True))
print("Percentage of classes in test set:")
print(y_test.value_counts(normalize=True))
Building the Model¶
Model evaluation criterion¶
Model can make wrong predictions as:¶
- Predicting an individual will accept a loan but in reality the individual did not accept the offered loan.-Loss of resources (FN)
- Predicting an individual won't accept a loan but in reality the individual did accept a loan . -Loss of opportunity (FP)
Which case is more important?¶
- If we predict an individual will accept a loan but actually the individual did not accept the loan - This is loss of resources as cost of the campaign would end up wasteful.
How to reduce this loss i.e need to reduce False Negatives?¶
Recallshould be maximized, the greater the recall higher the chances of minimizing the false negatives
Creating functions to calculate different metrics and confusion matrix so that we don't have to use the same code repeatedly for each model.¶
In [62]:
def model_performance_classification_sklearn_with_threshold(model, predictors, target, threshold=0.5):
"""
Function to compute different metrics, based on the threshold specified, to check classification model performance
model: classifier
predictors: independent variables
target: dependent variable
threshold: threshold for classifying the observation as class 1
"""
# predicting using the independent variables
pred_prob = model.predict_proba(predictors)[:, 1]
pred_thres = pred_prob > threshold
pred = np.round(pred_thres)
acc = accuracy_score(target, pred) # to compute Accuracy
recall = recall_score(target, pred) # to compute Recall
precision = precision_score(target, pred) # to compute Precision
f1 = f1_score(target, pred) # to compute F1-score
# creating a dataframe of metrics
df_perf = pd.DataFrame(
{
"Accuracy": acc,
"Recall": recall,
"Precision": precision,
"F1": f1,
},
index=[0],
)
return df_perf
In [63]:
# defining a function to plot the confusion_matrix of a classification model built using sklearn
def confusion_matrix_sklearn_with_threshold(model, predictors, target, threshold=0.5):
"""
To plot the confusion_matrix, based on the threshold specified, with percentages
model: classifier
predictors: independent variables
target: dependent variable
threshold: threshold for classifying the observation as class 1
"""
pred_prob = model.predict_proba(predictors)[:, 1]
pred_thres = pred_prob > threshold
y_pred = np.round(pred_thres)
cm = confusion_matrix(target, y_pred)
labels = np.asarray(
[
["{0:0.0f}".format(item) + "\n{0:.2%}".format(item / cm.flatten().sum())]
for item in cm.flatten()
]
).reshape(2, 2)
plt.figure(figsize=(6, 4))
sns.heatmap(cm, annot=labels, fmt="")
plt.ylabel("True label")
plt.xlabel("Predicted label")
Logistic Regression¶
In [64]:
# There are different solvers available in Sklearn logistic regression
# The newton-cg solver is faster for high-dimensional data
lg = LogisticRegression(solver="newton-cg", random_state=1)
model = lg.fit(X_train, y_train)
Finding the coefficients¶
In [65]:
coef_df = pd.DataFrame(
np.append(lg.coef_, lg.intercept_),
index=X_train.columns.tolist() + ["Intercept"],
columns=["Coefficients"],
)
coef_df.T
Out[65]:
Coefficient of Interpretations¶
- Coefficient of Age, Income, Family,CCAvg,Education,Mortgage, CD_Accounts and some regions are positive, an increase in these will lead to increases in chances of a person to accept a loan.
- Coefficient of Securities_Account, Online, CreditCard and some regions as negative, an increase in these will lead to decrease of chances of a person to accept a loan.
Converting Coefficient to Odds¶
In [66]:
# converting coefficients to odds
odds = np.exp(lg.coef_[0])
# finding the percentage change
perc_change_odds = (np.exp(lg.coef_[0]) - 1) * 100
# removing limit from number of columns to display
pd.set_option("display.max_columns", None)
# adding the odds to a dataframe
pd.DataFrame({"Odds": odds, "Change_odd%": perc_change_odds}, index=X_train.columns).T
Out[66]:
Coefficient interpretations¶
Age: Holding all other features constant a 1 unit change in Age will increase the odds of a person to accept a loan by 1 times or a 0.43% increase in odds of accepting a loan.Income: Holding all other features constant a 1 unit change in Income will increase the odds of a person to accept a loan by 1.3 times or a 28.8% increase in odds of accepting a loan.Family: Holding all other features constant a 1 unit change in Family will increase the odds of a person to accept a loan by 1.8 times or a 84.8% increase in odds of accepting a loan.CCAvg: Holding all other features constant a 1 unit change in CCAvg will increase the odds of a person to accept a loan by 2.5 times or a 154% increase in odds of accepting a loan.Education: Holding all other features constant a 1 unit change in Education will increase the odds of a person to accept a loan by 3.8 times or a 278% increase in odds of accepting a loan.Mortgage: Holding all other features constant a 1 unit change in Mortgage will increase the odds of a person to accept a loan by 1 times or a 0.15% increase in odds of accepting a loan.Securities Account: Holding all other features constant a 1 unit change in Securities Account will increase the odds of a person to accept a loan by 0.35 times but will have a 64% decrease in odds of accepting a loan.CD Account: Holding all other features constant a 1 unit change in CD Account will increase the odds of a person to accept a loan by 23.8 times or a 2283% increase in odds of accepting a loan.Online: Holding all other features constant a 1 unit change in Online will increase the odds of a person to accept a loan by 0.65 times but will have a 34% decrease in odds of accepting a loan.CreditCard: Holding all other features constant a 1 unit change in CreditCard will increase the odds of a person to accept a loan by 0.32 times but will have a 68% decrease in odds of accepting a loan.Regional_tier: Holding all other features constant a 1 unit change will follow same interpretations based on the odd and change_odd% values.
Interpretation for other attributes can be done similarly.
Checking model performance on training set¶
In [67]:
# creating confusion matrix
confusion_matrix_sklearn_with_threshold(lg, X_train, y_train)
In [68]:
log_reg_model_train_perf = model_performance_classification_sklearn_with_threshold(
lg, X_train, y_train
)
print("Training performance:")
log_reg_model_train_perf
Out[68]:
Checking model performance on testing set¶
In [69]:
# creating confusion matrix
confusion_matrix_sklearn_with_threshold(lg, X_test, y_test)
In [70]:
log_reg_model_test_perf = model_performance_classification_sklearn_with_threshold(
lg, X_test, y_test
)
print("Test set performance:")
log_reg_model_test_perf
Out[70]:
ROC-AUC¶
- ROC-AUC on training set
In [71]:
logit_roc_auc_train = roc_auc_score(y_train, lg.predict_proba(X_train)[:, 1])
fpr, tpr, thresholds = roc_curve(y_train, lg.predict_proba(X_train)[:, 1])
plt.figure(figsize=(7, 5))
plt.plot(fpr, tpr, label="Logistic Regression (area = %0.2f)" % logit_roc_auc_train)
plt.plot([0, 1], [0, 1], "r--")
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.05])
plt.xlabel("False Positive Rate")
plt.ylabel("True Positive Rate")
plt.title("Receiver operating characteristic")
plt.legend(loc="lower right")
plt.show()
- ROC- AUC on testing set
In [72]:
logit_roc_auc_test = roc_auc_score(y_test, lg.predict_proba(X_test)[:, 1])
fpr, tpr, thresholds = roc_curve(y_test, lg.predict_proba(X_test)[:, 1])
plt.figure(figsize=(7, 5))
plt.plot(fpr, tpr, label="Logistic Regression (area = %0.2f)" % logit_roc_auc_test)
plt.plot([0, 1], [0, 1], "r--")
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.05])
plt.xlabel("False Positive Rate")
plt.ylabel("True Positive Rate")
plt.title("Receiver operating characteristic")
plt.legend(loc="lower right")
plt.show()
- ROC-AUC Score for both training and testing set are high, showing we have a good model classifier.
- Model shows no signs of overfitting or underfitting, however, there's need to optimize the recall metric so as to minimize the False Negatives.
Model Performance Improvement¶
- Let's see if the Recall score and other metrics can be improved further, by changing the model threshold using AUC-ROC Curve.
Optimal threshold using AUC-ROC curve¶
In [73]:
# Optimal threshold as per AUC-ROC curve
# The optimal cut off would be where tpr is high and fpr is low
fpr, tpr, thresholds = roc_curve(y_train, lg.predict_proba(X_train)[:, 1])
optimal_idx = np.argmax(tpr - fpr)
optimal_threshold_auc_roc = thresholds[optimal_idx]
print(optimal_threshold_auc_roc)
Checking model performance on training set¶
In [74]:
# creating confusion matrix
confusion_matrix_sklearn_with_threshold(
lg, X_train, y_train, threshold=optimal_threshold_auc_roc
)
In [75]:
# checking model performance for this model
log_reg_model_train_perf_threshold_auc_roc = (
model_performance_classification_sklearn_with_threshold(
lg, X_train, y_train, threshold=optimal_threshold_auc_roc
)
)
print("Training performance:")
log_reg_model_train_perf_threshold_auc_roc
Out[75]:
Checking model performance on testing set¶
In [76]:
# creating confusion matrix
confusion_matrix_sklearn_with_threshold(
lg, X_test, y_test, threshold=optimal_threshold_auc_roc
)
In [77]:
# checking model performance for this model
log_reg_model_test_perf_threshold_auc_roc = (
model_performance_classification_sklearn_with_threshold(
lg, X_test, y_test, threshold=optimal_threshold_auc_roc
)
)
print("Test set performance:")
log_reg_model_test_perf_threshold_auc_roc
Out[77]:
- Recall value for both training and testing set increased signifcantly. However,Precision and F1 score declined.
- There is need to find a better threshold so as to have improve evaluation metric while keeping the recall metric in mind.
Let's use Precision-Recall curve and see if we can find a better threshold¶
In [78]:
y_scores = lg.predict_proba(X_train)[:, 1]
prec, rec, tre = precision_recall_curve(
y_train,
y_scores,
)
def plot_prec_recall_vs_tresh(precisions, recalls, thresholds):
plt.plot(thresholds, precisions[:-1], "b--", label="precision")
plt.plot(thresholds, recalls[:-1], "g--", label="recall")
plt.xlabel("Threshold")
plt.legend(loc="upper left")
plt.ylim([0, 1])
plt.figure(figsize=(10, 7))
plot_prec_recall_vs_tresh(prec, rec, tre)
plt.show()
- At the threshold of 0.38, we get balanced recall and precision.
In [79]:
# setting the threshold
optimal_threshold_curve = 0.38
Checking performance of training set¶
In [80]:
# creating confusion matrix
confusion_matrix_sklearn_with_threshold(
lg, X_train, y_train, threshold=optimal_threshold_curve
)
In [81]:
log_reg_model_train_perf_threshold_curve = (
model_performance_classification_sklearn_with_threshold(
lg, X_train, y_train, threshold=optimal_threshold_curve
)
)
print("Training performance:")
log_reg_model_train_perf_threshold_curve
Out[81]:
Checking model performance of test set¶
In [82]:
# creating confusion matrix
confusion_matrix_sklearn_with_threshold(
lg, X_test, y_test, threshold=optimal_threshold_curve
)
In [83]:
log_reg_model_test_perf_threshold_curve = (
model_performance_classification_sklearn_with_threshold(
lg, X_test, y_test, threshold=optimal_threshold_curve
)
)
print("Test set performance:")
log_reg_model_test_perf_threshold_curve
Out[83]:
- At the threshold value of 0.38, value for both Recall and Precision is balanced
- Generalized model attained also attained.
Model Performance Summary¶
In [84]:
# training performance comparison
models_train_comp_df = pd.concat(
[
log_reg_model_train_perf.T,
log_reg_model_train_perf_threshold_auc_roc.T,
log_reg_model_train_perf_threshold_curve.T,
],
axis=1,
)
models_train_comp_df.columns = [
"Logistic Regression sklearn",
"Logistic Regression-0.14 Threshold",
"Logistic Regression-0.38 Threshold",
]
print("Training performance comparison:")
models_train_comp_df
Out[84]:
In [85]:
# testing performance comparison
models_test_comp_df = pd.concat(
[
log_reg_model_test_perf.T,
log_reg_model_test_perf_threshold_auc_roc.T,
log_reg_model_test_perf_threshold_curve.T,
],
axis=1,
)
models_test_comp_df.columns = [
"Logistic Regression sklearn",
"Logistic Regression-0.14 Threshold",
"Logistic Regression-0.38 Threshold",
]
print("Test set performance comparison:")
models_test_comp_df
Out[85]:
Conclusion For Logistic Regression¶
- I have been able to build a predictive model that can be used by the bank to acquire customers to accept loans
- Without improving the model metrics, the area in ROC curve of 0.96 which is close to 1 shows the model has a good classifier.
- Coefficient of Age, Income, Family,CCAvg,Education,Mortgage, CD_Accounts and some regions are positive, an increase in these will lead to increases in chances of a person to accept a loan.
- Coefficient of Securities_Account, Online, CreditCard and some regions as negative, an increase in these will lead to decrease of chances of a person to accept a loan.
- Using the Precision Recall curve threshold method, recall value was improved significantly from 0.57 to 0.74 on the test set.
Decision Tree Model¶
In [89]:
# defining a function to compute different metrics to check performance of a classification model built using sklearn
def model_performance_classification_sklearn(model, predictors, target):
"""
Function to compute different metrics to check classification model performance
model: classifier
predictors: independent variables
target: dependent variable
"""
# predicting using the independent variables
pred = model.predict(predictors)
acc = accuracy_score(target, pred) # to compute Accuracy
recall = recall_score(target, pred) # to compute Recall
precision = precision_score(target, pred) # to compute Precision
f1 = f1_score(target, pred) # to compute F1-score
# creating a dataframe of metrics
df_perf = pd.DataFrame(
{
"Accuracy": acc,
"Recall": recall,
"Precision": precision,
"F1": f1,
},
index=[0],
)
return df_perf
In [90]:
def confusion_matrix_sklearn(model, predictors, target):
"""
To plot the confusion_matrix with percentages
model: classifier
predictors: independent variables
target: dependent variable
"""
y_pred = model.predict(predictors)
cm = confusion_matrix(target, y_pred)
labels = np.asarray(
[
["{0:0.0f}".format(item) + "\n{0:.2%}".format(item / cm.flatten().sum())]
for item in cm.flatten()
]
).reshape(2, 2)
plt.figure(figsize=(6, 4))
sns.heatmap(cm, annot=labels, fmt="")
plt.ylabel("True label")
plt.xlabel("Predicted label")
In [91]:
model = DecisionTreeClassifier(
criterion="gini", class_weight={0: 0.10, 1: 0.90}, random_state=1
)
In [92]:
model.fit(X_train, y_train)
Out[92]:
Checking model on training set¶
In [93]:
confusion_matrix_sklearn(model, X_train, y_train)
In [94]:
decision_tree_perf_train = model_performance_classification_sklearn(
model, X_train, y_train
)
decision_tree_perf_train
Out[94]:
Checking model performance on test set¶
In [95]:
confusion_matrix_sklearn(model, X_test, y_test)
In [96]:
decision_tree_perf_test = model_performance_classification_sklearn(
model, X_test, y_test
)
decision_tree_perf_test
Out[96]:
- There is a slight disparity in performance of model on training set and test set, which suggests that the model is showing signs overfiiting.
- Trees built needs pruning.
Visualize the Decision Tree¶
In [98]:
column_names = list(X.columns)
feature_names = column_names
print(feature_names)
In [99]:
plt.figure(figsize=(20, 30))
out = tree.plot_tree(
model,
feature_names=feature_names,
filled=True,
fontsize=9,
node_ids=True,
class_names=True,
)
for o in out:
arrow = o.arrow_patch
if arrow is not None:
arrow.set_edgecolor("black")
arrow.set_linewidth(1)
plt.show()
In [100]:
# Text report showing the rules of a decision tree -
print(tree.export_text(model, feature_names=feature_names, show_weights=True))
- The tree above is very complex and difficult to interpret.
In [101]:
importances = model.feature_importances_
indices = np.argsort(importances)
plt.figure(figsize=(12, 12))
plt.title("Feature Importances")
plt.barh(range(len(indices)), importances[indices], color="violet", align="center")
plt.yticks(range(len(indices)), [feature_names[i] for i in indices])
plt.xlabel("Relative Importance")
plt.show()
- According to the decision tree model, Income is the most important variable for predicting loan acceptance.
Using GridSearch for Hyperparameter tuning of our tree model¶
- Let's see if we can improve our model performance even more and reduce overfitting.
In [102]:
# Choose the type of classifier.
estimator = DecisionTreeClassifier(random_state=1)
# Grid of parameters to choose from
parameters = {
"max_depth": [5, 10, 15, None],
"criterion": ["entropy", "gini"],
"splitter": ["best", "random"],
"min_impurity_decrease": [0.00001, 0.0001, 0.01],
}
# Type of scoring used to compare parameter combinations
acc_scorer = make_scorer(recall_score)
# Run the grid search
grid_obj = GridSearchCV(estimator, parameters, scoring=acc_scorer, cv=5)
grid_obj = grid_obj.fit(X_train, y_train)
# Set the clf to the best combination of parameters
estimator = grid_obj.best_estimator_
# Fit the best algorithm to the data.
estimator.fit(X_train, y_train)
Out[102]:
Checking model performace on the training set¶
In [103]:
decision_tree_tune_perf_train = model_performance_classification_sklearn(
estimator, X_train, y_train
)
decision_tree_tune_perf_train
Out[103]:
In [104]:
confusion_matrix_sklearn(estimator, X_train, y_train)
Checking model performance on testing set¶
In [105]:
decision_tree_tune_perf_test = model_performance_classification_sklearn(
estimator, X_test, y_test
)
decision_tree_tune_perf_test
Out[105]:
- The model is giving a generalized result now.
Visualizing the Decision Tree¶
In [106]:
## creating a list of column names
feature_names = X_train.columns.to_list()
In [108]:
plt.figure(figsize=(15, 10))
out = tree.plot_tree(
estimator,
feature_names=feature_names,
filled=True,
fontsize=9,
node_ids=False,
class_names=None,
)
for o in out:
arrow = o.arrow_patch
if arrow is not None:
arrow.set_edgecolor("black")
arrow.set_linewidth(1)
plt.show()
- Tree built is much more simpler and overfitting has been treated
In [110]:
# importance of features in the tree building ( The importance of a feature is computed as the
# (normalized) total reduction of the 'criterion' brought by that feature. It is also known as the Gini importance )
print(
pd.DataFrame(
estimator.feature_importances_, columns=["Imp"], index=X_train.columns
).sort_values(by="Imp", ascending=False)
)
# Here we will see that importance of features has increased
In [111]:
importances = estimator.feature_importances_
indices = np.argsort(importances)
plt.figure(figsize=(12, 12))
plt.title("Feature Importances")
plt.barh(range(len(indices)), importances[indices], color="violet", align="center")
plt.yticks(range(len(indices)), [feature_names[i] for i in indices])
plt.xlabel("Relative Importance")
plt.show()
- Income, Education and Family are the top 3 strong predictors to determine if a customer will accept a loan or not.
Cost Complexity Pruning¶
In [112]:
clf = DecisionTreeClassifier(random_state=1)
path = clf.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas, impurities = path.ccp_alphas, path.impurities
In [113]:
pd.DataFrame(path)
Out[113]:
In [114]:
fig, ax = plt.subplots(figsize=(15, 5))
ax.plot(ccp_alphas[:-1], impurities[:-1], marker="o", drawstyle="steps-post")
ax.set_xlabel("effective alpha")
ax.set_ylabel("total impurity of leaves")
ax.set_title("Total Impurity vs effective alpha for training set")
plt.show()
In [115]:
clfs = []
for ccp_alpha in ccp_alphas:
clf = DecisionTreeClassifier(random_state=1, ccp_alpha=ccp_alpha)
clf.fit(X_train, y_train)
clfs.append(clf)
print(
"Number of nodes in the last tree is: {} with ccp_alpha: {}".format(
clfs[-1].tree_.node_count, ccp_alphas[-1]
)
)
Removing the last element in
clfs and ccp_alphas, because it is the trivial tree with only one
node. Here we show that the number of nodes and tree depth decreases as alpha
increases.
In [116]:
clfs = clfs[:-1]
ccp_alphas = ccp_alphas[:-1]
node_counts = [clf.tree_.node_count for clf in clfs]
depth = [clf.tree_.max_depth for clf in clfs]
fig, ax = plt.subplots(2, 1, figsize=(10, 7))
ax[0].plot(ccp_alphas, node_counts, marker="o", drawstyle="steps-post")
ax[0].set_xlabel("alpha")
ax[0].set_ylabel("number of nodes")
ax[0].set_title("Number of nodes vs alpha")
ax[1].plot(ccp_alphas, depth, marker="o", drawstyle="steps-post")
ax[1].set_xlabel("alpha")
ax[1].set_ylabel("depth of tree")
ax[1].set_title("Depth vs alpha")
fig.tight_layout()
Recall vs alpha for training and testing sets¶
In [117]:
recall_train = []
for clf in clfs:
pred_train = clf.predict(X_train)
values_train = recall_score(y_train, pred_train)
recall_train.append(values_train)
In [118]:
recall_test = []
for clf in clfs:
pred_test = clf.predict(X_test)
values_test = recall_score(y_test, pred_test)
recall_test.append(values_test)
In [119]:
fig, ax = plt.subplots(figsize=(15, 5))
ax.set_xlabel("alpha")
ax.set_ylabel("Recall")
ax.set_title("Recall vs alpha for training and testing sets")
ax.plot(ccp_alphas, recall_train, marker="o", label="train", drawstyle="steps-post")
ax.plot(ccp_alphas, recall_test, marker="o", label="test", drawstyle="steps-post")
ax.legend()
plt.show()
In [120]:
# creating the model where we get highest train and test recall
index_best_model = np.argmax(recall_test)
best_model = clfs[index_best_model]
print(best_model)
Checking the model performance on training set¶
In [121]:
decision_tree_postpruned_perf_train = model_performance_classification_sklearn(
best_model, X_train, y_train
)
decision_tree_postpruned_perf_train
Out[121]:
In [122]:
confusion_matrix_sklearn(best_model, X_train, y_train)
Checking the model performance on the testing set¶
In [123]:
decision_tree_postpruned_perf_test = model_performance_classification_sklearn(
best_model, X_test, y_test
)
decision_tree_postpruned_perf_test
Out[123]:
- A more generalized model performance on both training and test set compared to pre-pruning method
- The recall has improved further.
Visualizing the Decision Tree¶
In [124]:
plt.figure(figsize=(10, 10))
out = tree.plot_tree(
best_model,
feature_names=feature_names,
filled=True,
fontsize=9,
node_ids=True,
class_names=True,
)
for o in out:
arrow = o.arrow_patch
if arrow is not None:
arrow.set_edgecolor("black")
arrow.set_linewidth(1)
plt.show()
plt.show()
In [125]:
# Text report showing the rules of a decision tree -
print(tree.export_text(best_model, feature_names=feature_names, show_weights=True))
In [126]:
# importance of features in the tree building ( The importance of a feature is computed as the
# (normalized) total reduction of the 'criterion' brought by that feature. It is also known as the Gini importance )
print(
pd.DataFrame(
best_model.feature_importances_, columns=["Imp"], index=X_train.columns
).sort_values(by="Imp", ascending=False)
)
In [127]:
importances = best_model.feature_importances_
indices = np.argsort(importances)
plt.figure(figsize=(12, 12))
plt.title("Feature Importances")
plt.barh(range(len(indices)), importances[indices], color="violet", align="center")
plt.yticks(range(len(indices)), [feature_names[i] for i in indices])
plt.xlabel("Relative Importance")
plt.show()
- Education came out tops for the post pruning method while income and Family like the pre-pruning area also significant predictors.
Comparing all the Decision Tree Models¶
In [128]:
# training performance comparison
models_train_comp_df = pd.concat(
[
decision_tree_perf_train.T,
decision_tree_tune_perf_train.T,
decision_tree_postpruned_perf_train.T,
],
axis=1,
)
models_train_comp_df.columns = [
"Decision Tree sklearn",
"Decision Tree (Pre-Pruning)",
"Decision Tree (Post-Pruning)",
]
print("Training performance comparison:")
models_train_comp_df
Out[128]:
In [129]:
# test performance comparison
models_train_comp_df = pd.concat(
[
decision_tree_perf_test.T,
decision_tree_tune_perf_test.T,
decision_tree_postpruned_perf_test.T,
],
axis=1,
)
models_train_comp_df.columns = [
"Decision Tree sklearn",
"Decision Tree (Pre-Pruning)",
"Decision Tree (Post-Pruning)",
]
print("Test set performance comparison:")
models_train_comp_df
Out[129]:
- Decision tree with post-pruning is giving the highest recall on the test set.
- The tree with post pruning is not complex and easy to interpret.
Comparing all the models for Logistic Regression and Decision Tree Models¶
In [131]:
# training performance comparison
models_train_comp_df = pd.concat(
[
log_reg_model_train_perf.T,
log_reg_model_train_perf_threshold_auc_roc.T,
log_reg_model_train_perf_threshold_curve.T,
decision_tree_perf_train.T,
decision_tree_tune_perf_train.T,
decision_tree_postpruned_perf_train.T,
],
axis=1,
)
models_train_comp_df.columns = [
"Logistic Regression sklearn",
"Logistic Regression-0.14 Threshold",
"Logistic Regression-0.38 Threshold",
"Decision Tree sklearn",
"Decision Tree (Pre-Pruning)",
"Decision Tree (Post-Pruning)",
]
print("Training performance comparison:")
models_train_comp_df
Out[131]:
In [132]:
# testing performance comparison
models_test_comp_df = pd.concat(
[
log_reg_model_test_perf.T,
log_reg_model_test_perf_threshold_auc_roc.T,
log_reg_model_test_perf_threshold_curve.T,
decision_tree_perf_test.T,
decision_tree_tune_perf_test.T,
decision_tree_postpruned_perf_test.T,
],
axis=1,
)
models_test_comp_df.columns = [
"Logistic Regression sklearn",
"Logistic Regression-0.14 Threshold",
"Logistic Regression-0.38 Threshold",
"Decision Tree sklearn",
"Decision Tree (Pre-Pruning)",
"Decision Tree (Post-Pruning)",
]
print("Testing performance comparison:")
models_test_comp_df
Out[132]:
Overall Conclusion/ Insights:¶
- The aim of the ALLLife bank is to convert there liability customers into loan customers. Decision Tree algorithm have the highest recall rate to minimize the False Negative, all other performance metrics are also suited with decision trees when compared with Logistic Regression.
- Income, Family and Education level of customers are the strongest predictors for converting liability customers into loan customers.
- The model built can be used to predict if a customer will accept a loan or not.
- The importance of hyper-parameters/ pruning to reduce overfitting was duly established.
- Income influences other predictors such as CCAvg, Mortgage, CD_Account and personal loan.
Recommendations¶
- For AllLife Bank to increase the conversions of liability customers into loan customers, campaign profile for customers should include the following : Customers with higher education, who owns CD Account, does not have securities account , does not have credit card and higher income greater than >55k.
- Family with size of 3 at the minimum, with mortgage value and higher income can also be targeted for higher conversions.
- Individuals with high income in North_Coast and Southern San Joaquin regions can also be targeted to increase conversion of customer to accept loan.
- For better resource management, Banks should consider strong predictors of income, education level, family size to create campaign artifacts.
- Going forward, bank management should strategically acquire potential customers who have all the required element of good income, education, family size so as to reduce the volume of liability customers and easily make money from loan interests.
In [ ]: